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Title: Preemptive parallel-machine scheduling with a common server to minimize makespan
Authors: Cheng, TCE 
Kravchenko, SA
Lin, BMT
Keywords: Scheduling
Parallel machines
Common server
Issue Date: 2017
Publisher: John Wiley & Sons
Source: Naval research logistics, 2017, v. 64, no. 5, p. 388-398 How to cite?
Journal: Naval research logistics 
Abstract: We consider parallel-machine scheduling with a common server and job preemption to minimize the makespan. While the non-preemptive version of the problem is strongly NP-hard, the complexity status of the preemptive version has remained open. We show that the preemptive version is NP-hard even if there is a fixed number of machines. We give a pseudo-polynomial time algorithm to solve the case with two machines. We show that the case with an arbitrary number of machines is unary NP-hard, analyze the performance ratios of some natural heuristic algorithms, and present several solvable special cases.
ISSN: 0894-069X
EISSN: 1520-6750
DOI: 10.1002/nav.21762
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